Question

In Hecksher - Ohlin Model, if product 1 is Capital intensive and product 2 is Labor intensive, why there is a positive relationship between w/r and K/L we should explain it by referring to cost minimization problem

Answer 1

According to Heckscher-Ohlin theorem: A country will export the good which is intensive in the factor that the country is relatively well endowed with and import the good which is intensive in the factor that the country is relatively scarcely endowed with.

Assume that the country has a fixed endowment of labor, L, and capital, K, and that these resources can be used only in the production of goods y₁ and y₂. The labor and capital are each homogeneous and are assumed to be freely and costlessly mobile between industries. The following resource constraints must then be satisfied.

Factor Intensity: Definition

Factor intensity is used to compare relative factor usage between industries. Thus, we would say that good one is capital-intensive compared with good two if,

That is, if good one uses more capital per worker in production than the amount of capital used per worker in the production of good two, then good one is capital-intensive.

Note also that if then, by rearranging, . This means that good two uses more labor per unit of capital in production than the amount of labor used per unit of capital in the production of good one. In other words, good two is labor-intensive. Thus, if good one is capital-intensive, it follows that good two is labor-intensive, and vice versa.

Consider the following two-stage process. In the first stage we minimize factor cost in production subject to a fixed level of production. In the second stage, we maximize output subject to the resource constraints.

First, rewrite the Lagrangian from above by reordering the terms to get,

Lamda = p1y1 + p2y2 +wL + rK

Now maximize by first individually minimizing the two sets of terms in brackets. That is,

Minimize

wrt. aL1 , aK1     y1 ( aL1 w + aK1 r )           and        Minimize

wrt. aL2 , aK2     y2 ( aL2 w + aK2 r )

subject to            f1 ( aL1 , aK1 ) = 1                             subject to,          f2 ( aL2 , aK2 ) = 1

Notice that yi aLi is simply the total amount of labor used to produce yi units while yi aKi is the total amount of capital needed to produce yi units. Thus, yi ( aLi w + aKi r ) = wLi + rKi and represents the total cost of producing yi units.

We saw that a rise in PT / PC raises w/r .This makes labor more expensive and naturally leads to substitution effects where each firm demands a higher K/L ratio I Note that for markets to clear this has to imply that the labor-intensive sector expands (intuition: PT rises) . There is therefore a positive relationship between w/r and K/L in both sectors.

Also please refer to this link for further detailed solution :

http://internationalecon.com/Trade/Tch115/T115-1.php

OR

http://homes.chass.utoronto.ca/~cdippel/LNHOV.pdf